Mathematics : asked on KpopJess
 22.05.2022

Math 283 Calculus III Chapter 16 curl and divergence

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09.07.2023, solved by verified expert
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Compute the curl:

Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31

Compute the divergence:

Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31

A conservative vector field has zero curl, which is not the case here, so Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31 is not conservative.

We can also employ the same method as I showed in an earlier question of yours [28193504]. We want to find a scalar function Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31 whose gradient is Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31, so

Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31

Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31

However, there is no function Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31 that depends only on Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31 and Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31 that satisfies this partial differential equation; to wit, we cannot eliminate Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31. So no such Math 283 Calculus III Chapter 16 curl and divergence, №18011280, 22.05.2022 20:31 exists.

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Mathematics
Step-by-step answer
P Answered by Specialist

Compute the curl:

\mathrm{curl} \vec F = \left(\dfrac{\partial}{\partial x} \, \vec\imath + \dfrac{\partial}{\partial y} \, \vec\jmath + \dfrac{\partial}{\partial z} \, \vec k\right) \times \left(xyz\,\vec\imath + yz\,\vec\jmath + xy\,\vec k\right) \\\\ ~~~~~~~~ = \left(\dfrac{\partial(xy)}{\partial y}-\dfrac{\partial(yz)}{\partial z}\right) \,\vec\imath + \left(\dfrac{\partial(xyz)}{\partial z} - \dfrac{\partial(xy)}{\partial x}\right) \,\vec\jmath + \left(\dfrac{\partial(yz)}{\partial x} - \dfrac{\partial(xyz)}{\partial y}\right) \, \vec k \\\\ ~~~~~~~~ = \boxed{(x - y) \,\vec\imath + (xy - y) \,\vec\jmath - xz\,\vec k}

Compute the divergence:

\mathrm{div} \vec F = \dfrac{\partial(xyz)}{\partial x} + \dfrac{\partial(yz)}{\partial y} + \dfrac{\partial (xy)}{\partial z} = yz + z + 0 = \boxed{(y+1)z}

A conservative vector field has zero curl, which is not the case here, so \vec F is not conservative.

We can also employ the same method as I showed in an earlier question of yours [28193504]. We want to find a scalar function f(x,y,z) whose gradient is \vec F, so

\dfrac{\partial f}{\partial x} = xyz \implies f(x,y,z) = \dfrac12 x^2yz + g(y,z)

\dfrac{\partial f}{\partial y} = yz = \dfrac12 x^2 z + \dfrac{\partial g}{\partial y}

However, there is no function g that depends only on y and z that satisfies this partial differential equation; to wit, we cannot eliminate x. So no such f exists.

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 

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